Question

The equation of the circle concentric with the circle $x ^ { 2 } + y ^ { 2 } - 4 x - 6 y - 3 = 0$ and touching y-axis, is.

• A. $x ^ { 2 } + y ^ { 2 } - 4 x - 6 y - 9 = 0$
• B. $x ^ { 2 } + y ^ { 2 } - 4 x - 6 y + 9 = 0$
• C. $x ^ { 2 } + y ^ { 2 } - 4 x - 6 y + 3 = 0$
• D. None of these

Answer 1

Answer: (B)

$x ^ { 2 } + y ^ { 2 } - 4 x - 6 y + 9 = 0$

Answer 2

Equation of circle concentric to given circle is

$x ^ { 2 } + y ^ { 2 } - 4 x - 6 y + k = 0$

It touches $x = 0$ , therefore

Radius = Perpendicular distance from centre to $x = 0$

$\Rightarrow \sqrt { 4 + 9 - k } = \frac { 2 } { \sqrt { 1 } } \Rightarrow k = 9$

Hence required equation is $x ^ { 2 } + y ^ { 2 } - 4 x - 6 y + 9 = 0$ .